Elastic stiffness moduli of hostun
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1 Ws s Vt e −−−−
∗∗∗∗ ====
γγγγ (5) 100 min
max max
∗ − − = e e e e Dr (6) Where Vt is the volume of the mould, γγγγ s was found to be 2.65 Kg/cm 3 , Ws the weight of the soil sample while emax and emin was found to be 1 and 0.656 respectively.
- 29 - 4.1.6. Limitations of Pluviation: There are some limitations on uniformity of the pluviated sand. If a sand has a wide range of particle sizes, horizontal and vertical segregation becomes apparent. The conclusion is that for well-graded sands, and sands that include a high percentage of fines, a uniform sample will not be produced. But it does not affect this research due to the uniformity of the sands used.
4.2.1. Brief explanation:
The Triaxial Test is widely used to assess soil resistance. Even though many other improvement machines have been introduced as for example the True Triaxial Test Apparatus that give better results close to the real soil behaviour, the standard Triaxial test is still performed. The main aim of this device is to know via different paths, how the ground responds to various stress states.
Different procedures can be adopted during the diverse stress and strain paths allowed in the triaxial test. The first step consists of applying a pressure to the fluid (normally water) inside the cell. An equal stress is felt by the soil sample in all the three directions and if the water inside the soil is allowed to come out this is called isotropic consolidation.
The second step consists of applying a vertical load on the top platen of the sample, which increases the axial stress. Normally the horizontal stress remains at the same value as in the beginning but both stresses may be modified by the tester. Testing can be carried out either under saturated conditions or under unsaturated conditions, and if the soil is saturated tests may be drained or undrained. All the experiments done in this research have been done without any vertical loading on dry Hostun sand.
- 30 - 4.2.2. Setting up:
The base of the Triaxial device was used to hold the split mould. Then the former was filled with sand by pluviation. So, as not to let the sand spread all over the holes and threads, some measures of prevention were carried out like sticking some tape on them. Once the mould was filled with sand, the porous stone was placed, and carefully aligned with the bender in the bottom platen, the top platen was positioned on there with the vertical bender element in (the bender on the bottom was used as a transmitter, the one on the top as a receiver). The membrane was then rolled up (with some grease applied to the platen), and two O-rings were clambed to the platens. Two plastic tubes coming from the top of the platen to the base were connected, and a 30KPa vacuum was applied inside the sample. It was then possible to remove the split mould.
Pic.7. After removing the split mould with a 30KPa vacuum on Once the sample had been set up, it was very important to check that the membrane had not any tiny hole in it that could allow air or water to get in. Providing the sand sample was perfectly sealed; there was no loss of vacuum when the tap was closed showing that the test could be continued. After fitting the horizontal B/E transducers through the membrane (explained later), the triaxial cell was assembled with the screws were tightened and the cell was filled up with water.
- 31 -
Pic.8. and 9. General view of the sample before and after putting on the cell and fill it with water.
In order to keep the same effective stress inside the specimen once the vacuum was switched off, a careful procedure needed to be followed. With the help of a pressure gauge and pressure regulator, a desired pressure can be introduced inside the cell. To not modify the sample stress, the pressures were adjusted step by step as follows:
- 32 - Vacuum Pressure Cell Pressure Effective Stress 30 KPa 0 KPa
30 KPa 20 KPa
20 KPa 40 KPa
10 KPa 30 KPa
40 KPa 0 KPa
30 KPa 30 KPa
One of the problems found at that point was that the gauges kept a 20KPa of pressure even though they were disconnected, so that is why an initial pressure of 30KPa was selected rather than a lower one. Finally the vacuum was switched off because the pressure inside the cell was reached and every tap was perfectly sealed ensuring there would not be any leak.
At this moment, inside the sample, the principal effective stresses were equal to σ x = σ y = σ
z = 30 KPa. As said before, that is the first step in the isotropic compression test, and in this case, the sand was not saturated. In order to assess the vertical deformation of the sample, the piston was set up (about 170mm diameter) with its tip in contact with the top platen housed on the top of the sand. Care was taken not to push the rod down because otherwise some extra deformation could be result. A dial gauge was set up on the top of the cell touching the piston to monitor the sample’s deformation during the test. Weights were applied to prevent the piston from moving up because of the cell pressure and therefore losing contact with the platen. The following table shows the weights required for various cell pressures.
Pressure (KPa) Weight (Kg) 30
0,85 60
1,7 90
2,55 120
3,4 150
4,25 180
5,1
- 33 - During the test, the drainage tap which connects to the interior of the sand sample was opened to allow the air out of the sand as the pressure in the cell was increased.
4.3.1. Introduction
Bender/Extender elements are plate-shaped transducers that can be mounted in the ends of the equipment or in the sides protruded as cantilevers into the soil sample. Their main aim is to send and receive shear/compression waves from which the shear/constrained wave velocities are found. Hence the shear/constrained modulus of a particular sample are calculated assuming elastic behaviour and body wave theory. Although there are several techniques to measure the shear modulus, as for example shear plates or the resonant column apparatus, it is concluded that this one enables the data to be obtained easily and, recent research has concentrated in the use of these new devices and in particular, their use in Triaxial equipment. In this work both vertical and horizontal transducers are protruded into the sand sample. The vertical ones were found to be easy to set up because specific platens were made to house them. However, the horizontal ones were hard to position; thus, some experimental improvements were performed as explained bellow.
It was decided to cut tiny slots (4 in total) with the shape of the horizontal benders (T shape) at roughly mid-height of the rubber membrane before pluviation was
- 34 - carried out. Therefore symmetrical cuts were made in both sides of the membrane, taking great care to align them perfectly so that, the transmitted and received waves will be entirely captured by the transducers. Then, some tape was stuck over them, so that, once the mould was filled up with the sand and the split mould was removed with the vacuum on, then using a very sharp knife, the cuts were reopened taking care not to make new unnecessary holes without the tape being removed. Once the holes were opened the horizontal transducers were quickly inserted into. A grommet was clamped to the bender pot by one O-ring, and the vacuum held the assembly against the wall of the specimen. After that, several layers of latex were applied on the boundaries of the grommet as shown in the following picture.
Pic.11. View of the several latex layers applied on the grommet with the horizontal bender/extender and one O-ring surrounding in order to stick it tight.
The Bender/Extender elements could not have been born without the piezoelectricity property. Piezoelectricity is found in nature in quartz and tourmaline crystals and it can be obtained artificially with certain ceramics such as lead zirconite, barium titanate and lead titanate. Piezoelectric materials exhibit a mechanical deformation when a voltage is applied or an electrical output when mechanically stressed.
- 35 - 4.3.3. How the transducers work:
A voltage applied to a piezoelectric material will cause a distortion, the orientation of which will depend on:
1. Voltage connection 2.
3.
Geometry of the material The transducers are made of bimorphs in which two sheets of piezoelectric material are fused together. Beginning with the bender transducers, it is seen that they can be polarized and connected in two different ways:
To the electrodes on the outside of each plate are connected to a voltage source and the plates are polarised in opposite direction. They develop twice the voltage of those connected in parallel for the same driving force and they provide only half the displacement of parallel elements for the same applied voltage. That is why they are always used as receivers.
Fig.5. Series connected and opposite direction of polarization for bender receivers - + Signal field Direction of polarization
- 36 -
The electrodes are on the outside of each plate, but these are connected together to the same terminal and the central conductor is connected to the other terminal. The plates are polarized in the same direction in this case. Bearing in mind the advantages and main drawbacks explained above this kind of connection is used for the transmitters transducers.
To understand the whole behaviour of the procedure a summarising is given step by step:
performed either using the time domain or the frequency domain. In this research no frequency domain measurements have been performed.
A Function Generation is used to create the desired waveform shape, frequency, voltage applied peak to peak and amplitude of the input wave. These are the principal parameters in the time domain and are the key to understand the final results. On one hand, this wave is recorded on the screen of a sophisticated oscilloscope, on the other hand, this input wave is sent via the transmitter charge amplifier to the transmitter - +
strain Signal field Direction of polarization
- 37 - element. As the transmitter bends (or extends) a shear or compressive wave is generated and through the specimen until it reaches the receiver transducer. This bends (or extends), as well, once the input wave arrives, and thus generates a voltage. After amplification, the output wave is also recorded on the oscilloscope device.
Fig.7. Line diagram showing the instrumentation connections to the B/E transducers, the oscilloscope, the charge amplifier and the sample.
Some initial tests were carried out under a 30KPa cell pressure and without any vertical deformation using a symmetrical sine pulse of 5KHz frequency. The following results were obtained:
- 38 - -15
-10 -5 0 5 10 15 0 0,0001
0,0002 0,0003
0,0004 0,0005
0,0006 0,0007
0,0008 0,0009
0,001 Travel time (us) in p u t (V ) -6,00E+01 -4,00E+01 -2,00E+01 0,00E+00 2,00E+01
4,00E+01 6,00E+01
o u tp u t (m V )
Fig.8. Behaviour of the Pvh .
-1,50E+01 -1,00E+01 -5,00E+00 0,00E+00
5,00E+00 1,00E+01
1,50E+01 0 0,0001 0,0002 0,0003
0,0004 0,0005
0,0006 0,0007
0,0008 0,0009
0,001 t i me ( us ) -8,00E+01 -6,00E+01 -4,00E+01 -2,00E+01 0,00E+00
2,00E+01 4,00E+01
6,00E+01 8,00E+01
Fig.9. Behaviour of the Svh.
- 39 - -10
-8 -6 -4 -2 0 2 4 6 8 10 0 0,0001 0,0002 0,0003
0,0004 0,0005
0,0006 0,0007
0,0008 0,0009
0,001 time (us) in p u t (V ) -350
-250 -150
-50 50 150 250 350
o u tp u t (m V )
Fig.10. Behaviour of the Shv. -10
-8 -6 -4 -2 0 2 4 6 8 10 0 0,0002 0,0004 0,0006
0,0008 0,001
0,0012 0,0014
0,0016 0,0018
0,002 time (us) in p u t (V ) -400
-300 -200
-100 0 100 200 300
400 o u tp u t (m V )
Fig.11. Behaviour of the Shh.
- 40 - -10
-8 -6 -4 -2 0 2 4 6 8 10 0 0,0002 0,0004 0,0006
0,0008 0,001
0,0012 0,0014
0,0016 0,0018
0,002 t i me ( us ) -20
-15 -10
-5 0 5 10 15 20 Fig.12.Behaviour of Phv wave.
-10
-8 -6 -4 -2 0 2 4 6 8 10 0 0,0001 0,0002 0,0003
0,0004 0,0005
0,0006 0,0007
0,0008 0,0009
0,001 time (us) in p u t (V ) -15
-10 -5 0 5 10 15 o u tp u t (m v )
Fig.13. Behaviour of Phh wave.
Here P and S denote compression and shear waves respectively, and Vh denotes a wave propagating vertically and polarised in a horizontal direction. These Pvh, Svh, Shv, Shh, Phv and Phh waves give us enough information to assess shear and constrained modulus. It is necessary to determine the travel time between the start of the input wave signal and the first arrival point of the output wave signal. However, it is sometimes difficult to identify which is the right point of the output wave due for some distortions created by Cross Talk and Near field Effects. Keeping that in mind, once the right judgment is taken shear and constrained modulus can be easily assessed by means of the equation (3) and (4).
- 41 - In order to choose the best input wave for the data, some factors have to be taken in account; it is assumed that the best wave will be the one which give us the clearest signal.
Choosing a frequency: The optimum frequency of excitation depends on many factors such as soil stiffness and the applied pressure in the cell. Even though there is no rule at all for choosing the best wave, some authors have reported their experience some ideas about which frequency to take. Brignoli et al 1996 noted that for shear wave measurements with specimens of between 100 to140 mm high, the most interpretable output waves occur in the range from 3 to 10 KHz. Jovocic et al 1996, observed that with a higher frequency a higher ratio R d (see below) was obtained. Although this is good because the near field effect (see section 4.3.4.) is less discernible, there is a limit frequency at which overshooting of the transmitting bender starts to occur, which means that the frequency is too high and the element can not follow the input wave.
R d is defined as:
Rd = d/λ = (d*f)/V s
(7)
where d = travel distance and λ = wave length
Hence the near field effect depends not only on the frequency of the signal but also on Vs. For a high Vs, which means stiffer material, the ratio Rd will be lower and therefore the near field effect will be clearly present. For stiffer materials the required frequency is higher and so the problem of overshooting becomes more important. In addition to this, a wave with a high frequency attenuates faster than one with a lower frequency in the same medium. Because of those two reasons, although the use of a high frequency seems to give clearest output signals, the choice is limited.
- 42 - Choosing a waveform:
Within the literature it is possible to find some agreement over when a shape wave needs to be selected. The function generator gives several options-the symmetrical sine pulse wave, the square wave, the triangular wave and the distorted one (fig.14,15,16.). From the author’s point of view with the experience gained from the practice and as well as reading advice from several authors, it can be seen that the best input waveform to get a clear signal is the symmetrical sine pulse wave. Thanks to its sinusoidal shape it is easier to choose the right rising point whereas the others deal with more subjectivity. Santamarina et al 1997 observed that the main advantage of using square functions is to corroborate the shear wave arrival by reversed polarity. When the polarity of the transmitted wave was reversed, the reversal of the polarity of the output signal was taken as demonstration of the true arrival time. However, P-waves generated at the sides of the bender element can reach the receiver by reflections at cell boundaries and its polarity can be reversed as well.
-15
-10 -5 0 5 10 15 0 0,0001
0,0002 0,0003
0,0004 0,0005
0,0006 0,0007
0,0008 0,0009
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